Schumer, McCain: Obama supports our immigration bill

4/16/13 4:46 PM EDT

White House Photo

Sens. John McCain and Chuck Schumer said they were encouraged after a meeting with President Obama at the White House Tuesday, saying he supports the immigration reform bill they plan to introduce tonight and hope to pass by June.

"We're feeling very good about this," Schumer said outside the West Wing. "The president's supportive of our proposal."

"The president realizes that everybody didn’t get what they wanted," McCain said. "We appreciate the president's support. We believe that that's important as we move forward with the process."

One of the things the president didn't want, Schumer said, was a trigger that tied the opening of a pathway to citizenship to tighter border security. But, he said, he and the other members of the Gang of 8 senators who brokered the legislation felt it was important to prevent a so-called third wave of immigrants, who would flood the country and require another immigration-reform bill in the future.

McCain credited the election in November with helping to build support for the measure, and he said it has a much better chance of succeeding than previous efforts.

"Most Americans support this proposal far more than did in 2007," he said.

Schumer noted that business, labor, religious groups, and organizations representing farm workers are "enthusiastically on board" this time. He said the pathway to citizenship contained in the bill requires payment of a fine and taxes owed to the IRS and going to the back of the line of immigrants seeking citizenship, a process that could take years. He said critics who are against amnesty will have no basis to criticize the bill.

"That’s not amnesty in anyone's book except for those people who would oppose any immigration," he said.

McCain cautioned that despite the progress that's been made, there is still much work to do.

"This is the beginning of the process not the end," he said.

Schumer said the group plans to introduce the bill tonight, and then the first hearings will be held Friday and Monday. The bill will go on the markup schedule Tuesday, with an open markup process likely in early May, he said, adding that he expects several more hearings will be held over the next several weeks before the bill makes it to a floor vote, he hopes by June.